Finite frequency H_∞ filtering for time-delay systems

This chapter studies the problem of finite frequency (FF) H-infinity filtering for continuous-time systems with a constant state delay. The FF specification is motivated by the fact that many practical signals have their energy within an FF range, while the standard H-infinity filter theory cannot directly handle this fact. Using the generalized Kalman-Yakubovich-Popov lemma and the Projection Lemma, delay-dependent and delay-independent FF bounded real lemmas (BRLs) in terms of linear matrix inequalities (LMIs) are proposed for FF H-infinity filtering performance analysis. To prove these BRLs, a frequency-domain proof based on the transfer function representation and a time-domain proof using the Lyapunov-Krasovskii method are presented, respectively. Based on the obtained BRLs, delay-dependent and delay-independent approaches in terms of LMIs are proposed for designing filters with a guaranteed FF H-infinity performance for continuous-time systems with a state delay. What’s more, the delay-partitioning idea is made use of to reduce the conservatism of the delay-dependent approach. Finally, two numerical examples are provided to illustrate the effectiveness and advantages of the filter design methods developed in the chapter.